Which API can I use for tracking the position of animal in one or more images?
FastAI is the most “out of the box” API for this type of task.

For video examples (and a little theory) check out the MOOC section of their site. 

Practical Deep Learning and Cutting Edge Deep Learning are the two sections most relevant to you. 

But if you want a working implementation check out this GitHub repo that implements SSD for your purposes. I can’t say how simple the API is but it does what you are seeking (in pure PyTorch).

note: FastAI was originally built on top of PyTorch (although they are expanding out now), so you’ll be using PyTorch and need a rough idea of how to work with tensors. Most of the challenges are already implemented in their api. Installing their library will automatically install PyTorch.